Statistics and Probability Problems with Solutionssample 3

More Problems on probability and statistics are presented. The answers to these problems are at the bottom of the page. problems included are about: probabilities, mutually exclusive events and addition formula of probability, combinations, binomial distributions, normal distributions, reading charts.

Problems

In a group of 40 people, 10 are healthy and every person the of the remaining 30 has either high blood pressure, a high level of cholesterol or both. If 15 have high blood pressure and 25 have high level of cholesterol,
a) how many people have high blood pressure and a high level of cholesterol?
If a person is selected randomly from this group, what is the probability that he/she
b) has high blood pressure (event A)?
c) has high level of cholesterol(event B)?
d) has high blood pressure and high level of cholesterol (event A and B)?
e) has either high blood pressure or high level of cholesterol (event A or B)?
f) Use the above to check the probability formula: P(A or B) = P(A) + P(B) - P(A and B).

A committee of 5 people is to be formed randomly from a group of 10 women and 6 men. Find the probability that the committee has
a) 3 women and 2 men.
a) 4 women and 1 men.
b) 5 women.
c) at least 3 women.

In a school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that
a) exactly 5 have access to the internet.
b) at least 6 students have access to the internet.

The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation of 10. A student from this group is selected randomly.
a) Find the probability that his/her grade is greater than 80.
b) Find the probability that his/her grade is less than 50.
c) Find the probability that his/her grade is between 50 and 80.
d) Approximately, how many students have grades greater than 80?

In a certain country last year a total of 500 million tons of trash was recycled. The chart below shows the distribution, in millions of tons, for the different types of trashes.
a) How many tons of Iron/Steel was recycled?
b) What percent of the recycled trash was glass?